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Stiind x∈(π,3π/2) si cosx = 2√6/5. Calculati sinx

Răspuns :

[tex]x este in cadranu III unde sin x \ \textless \ 0., deci.sin x= - \sqrt{1- cos^{2}x [/tex]

Deci sin x = -[tex] \sqrt{1- cos^{2} x} = - \sqrt{1- ( \frac{ 2\sqrt{6} }{6} ) ^{2} [/tex] 
Obtinem: sin x= -[tex] \sqrt{1- \frac{24}{25} }= -\sqrt{ \frac{1}{25} } = - \frac{1}{5}. [/tex]